Monitoring thermal therapies through medical imaging is essential in order to ensure that they are safe, efficient and reliable. In this paper, we propose a new approach, halfway between MR acoustic radiation force imaging (MR-ARFI) and MR elastography (MRE), allowing for the quantitative measurement of the elastic modulus of tissue in a highly localized manner. It relies on the simulation of the MR-ARFI profile, which depends on tissue biomechanical properties, and on the identification of tissue elasticity through the fitting of experimental displacement images measured using rapid MR-ARFI. This method was specifically developed to monitor MR-guided high intensity focused ultrasound (MRgHIFU) therapy. Elasticity changes were followed during HIFU ablations (N = 6) performed ex vivo in porcine muscle samples, and were compared to temperature changes measured by MR-thermometry. Shear modulus was found to increase consistently and steadily a few seconds after the heating started, and such changes were found to be irreversible. The shear modulus was found to increase from 1.49 ± 0.48 kPa (before ablation) to 3.69 ± 0.93 kPa (after ablation and cooling). Thanks to its ability to perform quantitative elasticity measurements in a highly localized manner around the focal spot, this method proved to be particularly attractive for monitoring HIFU ablations.